Polarity of a bond arises due to difference in electronegativity of the bonded atoms. Electronegativity is the ability of an atom to attract electrons towards itself.

Electronegativity of Br = 2.8

Electronegativity of Cl = 3.0

Electronegativity of I = 2.5

The difference in electronegativity between Br and Cl is 0.2, while the difference in electronegativity between Br and I is 0.3.

Since the difference in electronegativity is greater for Br-Cl bond, it is more polar than Br-I bond.